Problem: Simplify the following expression: $ r = \dfrac{2z - 8}{-4z} + \dfrac{-2}{9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{2z - 8}{-4z} \times \dfrac{9}{9} = \dfrac{18z - 72}{-36z} $ Multiply the second expression by $\dfrac{-4z}{-4z}$ $ \dfrac{-2}{9} \times \dfrac{-4z}{-4z} = \dfrac{8z}{-36z} $ Therefore $ r = \dfrac{18z - 72}{-36z} + \dfrac{8z}{-36z} $ Now the expressions have the same denominator we can simply add the numerators: $r = \dfrac{18z - 72 + 8z}{-36z} $ $r = \dfrac{26z - 72}{-36z}$ Simplify the expression by dividing the numerator and denominator by -2: $r = \dfrac{-13z + 36}{18z}$